Excitation and Measurement Patterns for the Identifiability of Directed Acyclic Graphs

TL;DR

This paper develops systematic excitation and measurement patterns for identifying dynamical networks with DAG topology, extending known conditions to include additional node types for guaranteed identifiability.

Contribution

It introduces new excitation and measurement requirements for certain nodes in DAGs and proposes a systematic design procedure for these patterns.

Findings

New conditions for node excitation and measurement in DAGs

A systematic procedure for designing EMPs ensuring identifiability

Extension of classical identifiability conditions to additional node types

Abstract

This paper deals with the design of Excitation and Measurement Patterns (EMP) for the identification of a class of dynamical networks whose topology has the structure of a Directed Acyclic Graph (DAG). In addition to the by now well known condition that the identifiabiltiy of any dynamical network requires that the sources be excited, the sinks be measured, and all other nodes be either excited or measured, we show that for DAGs two other types of nodes have special excitation and measurement requirements. Armed with this result, we propose a systematic procedure for the design of EMPs that guarantee identifiability of a network with DAG topology.